If you're getting alot of ring or alot of the

of the top head, try this, take you're microphone and instead of pointing it down at the snare head place the mic as if you're micing the shell. Then raise it so maybe half the capsule is poking over the top of the head. Also I recommend the mic being back from the rim about an inch. Take a second mic and point it at the shell, down lower on the drum. Adjust the phase if need be, voila! very little head

and a nice snappy sound. If you're still getting some ringing
you can try alittle moongel, but this should get you there